fast.graph.param.estimator: Degree-based graph parameter estimator

In statGraph: Statistical Methods for Graphs

Description

fast.graph.param.estimator estimates the parameter of the complex network model using the degree-based spectral density and ternary search.

Usage

fast.graph.param.estimator(
  G,
  model,
  lo = NULL,
  hi = NULL,
  eps = 0.001,
  from = NULL,
  to = NULL,
  npoints = 2000,
  numCores = 1
)

Arguments

G	The undirected unweighted graph (igraph type).
model	Either a string or a function: A string that indicates one of the following models: "ER" (Erdos-Renyi random graph model), "GRG" (geometric random graph model), "WS" (Watts-Strogatz model), and "BA" (Barabasi-Albert model). A function that returns a Graph generated by a graph model. It must contain two arguments: the first one corresponds to the graph size and the second to the parameter of the model.
lo	Smallest parameter value that the graph model can take. If “model” is an string, then the default value of 0 is used for the predefined models ("ER", "GRG", "WS", and "BA").
hi	Largest parameter value that the graph model can take. If “model” is an string, then the default values are used for the predefined models 1 for "ER", sqrt(2) for "GRG", 1 for "WS", and 5 for "BA").
eps	Desired precision of the parameter estimate.
from	Lower end of the interval that contain the eigenvalues to generate the degree-based spectral densities. The smallest eigenvalue of the adjacency matrix corresponding to “graph” is used if the value is not given.
to	Upper end of the interval that contain the eigenvalues to generate the degree-based spectral densities. The largest eigenvalue of the adjacency matrix corresponding to “graph” is used if the value is not given.
npoints	Number of points to discretize the interval <from,to>.
numCores	Number of cores to use for parallelization.

Value

Returns a list containing:

param	The degree-based parameter estimate. For the "ER", "GRG", "WS", and "BA" models, the parameter corresponds to the probability to connect a pair of vertices, the radius used to construct the geometric graph in a unit square, the probability to reconnect a vertex, and the scaling exponent respectively.
L1_dist	The L1 distance between the observed graph and the graph model with the estimated value.

Examples

set.seed(42)

### Example giving only the name of the model to use
G <- igraph::sample_smallworld(dim = 1, size = 15, nei = 2, p = 0.2)

# Obtain the parameter of the WS model
estimated.parameter1 <- fast.graph.param.estimator(G, "WS", lo = 0.1, hi = 0.5,
                                                  eps = 1e-1, npoints = 10,
                                                  numCores = 1)
estimated.parameter1

## Not run: 
### Example giving a function instead of a model

# Defining the model to use
G <- igraph::sample_smallworld(dim = 1, size = 5000, nei = 2, p = 0.2)
K <- as.integer(igraph::ecount(G)/igraph::vcount(G))
fun_WS <- function(n, param, nei = K){
 return (igraph::sample_smallworld(dim = 1,size = n, nei = nei, p = param))
}

# Obtain the parameter of the WS model
estimated.parameter2 <- fast.graph.param.estimator(G, fun_WS, lo = 0.0, hi = 1.0,
                                                   npoints = 100, numCores = 2)
estimated.parameter2

## End(Not run)

statGraph documentation built on May 19, 2021, 9:11 a.m.